Europe bike insurance
I bought a Yam Diversion 900 in the UK three years ago and kept it for a few years of yearly riding there in the alps. Sensational, and the bike passed through a variety of friends hands before being given away last year, thrashed, crashed but still running (more or less) 30,000k later.
The insurance is complex and a hassle (you already know this). I bought the bike in a friends name who is a UK resident. He also has a bike licence (this is important). He insured it and added me as an extra rider.
However, most of the insurance brokers i tried (most insurance there is bought from brokers rather than direct eg Carole Nash is a broker) would not give my friend insurance with me as a rider as their systems did not cope with it.
One we found that did was Footman James who were fine to deal with. I only got third party which in Europe means combined third party property damage and personal injury to others.
Under EU law any insurance issued in a member country must be valid in any other EU country. So once you are insured in the UK (or wherever) you are insured to the minimum legal necessary level in all EU countries.
However, the cover outside the EU varies from policy to policy. Mine i discovered belatedly half way through Croatia didnt cover Croatia (it wasnt in the EU). I remedied this after much stuffing around by buying local cover for a month at a pretty reasonable price.. but to do this i had to go to a decent size town Zadar and find the insurance inspection depot (like our RTA inspection office) run by EuroHerc or something.
The yam was a 'walk away' bike for me - it cost 1000 pounds so if i binned it big time or had a major breakdown i was planning to walk away if i couldnt fix it. I didnt take breakdown cover which is usually an option on most bike insurance.
Also most insurance companies want to know if you are going outside the country of issue for more than 20 or 30 days continuous. Given the lack of border controls and the fact that bikes are no longer mentioned in passport stamps the insurance company is probably not going to know if you have been out of the UK for 10, 20 or 50 days if you make a claim. I ended up leaving the bike in a shed in Italy for 9 months but as far as the insurance company was concerned it was in the UK.
You will also need a valid MOT (roadworthiness certificate) which you get after an inspection. Unlike here this is not timed to coordinate with renewal of insurance or tax. So if you are taking a bike to another EU country for some months make sure you get a new MOT before you go if you will be out of the UK when it expires. It will be a condition of insurance that the bike has a current MOT for cover to be effective.
Is it all worth it....? Absolutely. Can you get by without the paperwork? Maybe if you are lucky. I got pulled over in Italy and the machine gun equipped cops wanted every bit of paper i had... they spread them all out in the back of their car and spent 20 mins going through it all cross checking. It hung togehter. Phew.
But amongs the papers they wanted were UK Registration Document (in my friends name - BTW there is a special process he/she will have to do for you to get a new one after buying a bike before going O/S) the insurance document with my name on it as a rider, passport, licence, etc etc. Because the bike was not in my name but i was rider i also had a signed letter from the legal owner (who is on the reg doc and insurance) giving me authority to ride it. The caribaniri loved that one.
Getting it all sorted can be a hassle cos nothing works like it should... but in the end i had a total of 20 weeks riding an ok bike with hard luggage for not too much (plus a ton of tyres).